There is a committee composed of eight women and two men. When they meet, they sit in a row---the women in indistinguishable rocking chairs and the men on indistinguishable stools. How many distinct ways are there for me to arrange the ten chairs and stools for a meeting?
I believe this is a similar problem to finding the number of distingiushable "words" that can be made from a "word" with repeated letters
Let each rocking chair be represented by the letter "A"
Let each stool be represented by the letter "B"
Then....we are looking for the number of distingiushable "words" that can made from the word
This is given by
_____ = 45 ways
8! * 2!